Generalization of Spectral Green's Function nodal method for slab-geometry fixed-source adjoint transport problems in S_N formulation

Presented here is the application of the adjoint technique for solving source{detector discrete ordinates (S_N) transport problems by using a spectral nodal method. For slab-geometry adjoint S-N model, the adjoint spectral Green's function method (SGF^†) is extended to multigroup problems considering arbitrary L'th-order of scattering anisotropy, and the possibility of non{zero prescribed boundary conditions for the forward S_N transport problems. The SGF^† method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF^† equations, we use the partial adjoint one{node block inversion (NBI) iterative scheme. Partial adjoint NBI scheme uses the most recent estimates for the node-edge adjoint angular Fluxes in the outgoing directions of a given discretization node, to solve the resulting adjoint SN problem in that node for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent node in the sweeping directions. Numerical results are given to illustrate the present spectral nodal method features and some advantages of using the adjoint technique in source-detector problems. author)